Please show the following question in detail, I don't understand one bit of it, " Let R be a relation defined on the set N by aRb if either a | 2b or b | 2a. Prove or disprove: R is an equivalence relation.

A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain of a relation R where 2 cars are related if they were made in the same year. b) Describe the partition defined by the equivalence classes. How do I do this?

3. Define a relation on the real numbers as follows: x Ry if and only if x² + y² = 1. Determine if R is reflexive, symmetric, and/or transitive. For each property, give sufficient justification for your answer.

This question confuses me, I dont get what is being asked? How do I approach this? "Let A be a nonempty set and let B be a subset of the power set P(A) of A. Define a relation R from A to B byxRY if x ∈ Y. Give an example of two sets A and B that illustrate this. What is R for these two sets?"

I am having trouble working thru this problem, any help would be appreciated.